Margaret Thatcher in Port Stanley, the Falkland Islands, during a visit to mark the 10th anniversary of the war. Photograph: Keith Waldegrave/Mail on Sunday/Rex Features

The death of Margaret Thatcher generated some of the most extreme reactions in Argentina and the Falkland Islands, which remain sharply divided by memories of the 1982 war.

By sending the British military to repel the invasion of the South Atlantic archipelago, the former prime minister earned the enduring thanks of the islanders, who continue to celebrate Thatcher Day every 10 January.

"She will be forever remembered in the islands for her decisiveness in sending a taskforce to liberate our home following the Argentine invasion in 1982," said Mike Summers, on behalf of the islands' legislative assembly. "Her friendship and support will be sorely missed, and we will always be thankful for all that she did for us."

Rosie King, a Port Stanley resident since before the 1982 war, said the island would arrange a memorial service and fly flags at half mast.

"She was probably the number one person in our history … It was mind-blowing when we heard on the radio that Thatcher would send a taskforce. When she arrived afterwards, it was like a visit from the Queen.

"I met her on a street corner and we chatted very comfortably. It wasn't like she was a big world leader. She wasn't as harsh as she was portrayed and she was smaller than I imagined … It was one of the most memorable moments of my life."

However, the Iron Lady stirred up very different sentiments in Argentina, where she is remembered as a war criminal who ordered the British submarine Conqueror to sink the General Belgrano even though it was outside the UK-declared exclusion zone. The resulting loss of 323 lives made up more than half the Argentinian casualties in the war.

"She will be remembered as a leader who gave nothing positive to humankind," said Ernesto Alberto Alonso, an Argentinian veteran of the war and president of the National Commission of Ex-Combatants of the Malvinas. "She was a person who caused not only great harm domestically but also internationally … In many ways, I think she was similar to the military dictatorship here, and in particular [General Leopoldo] Galtieri."

Argentina's president, Cristina Fernández de Kirchner – a fierce critic of Britain's policy towards the islands – has yet to comment on Thatcher's death, but the local media gave extensive and largely negative coverage.

The state news agency Telam classified as a war crime Thatcher's decision to sink the Belgrano.

"One less genocide criminal in the world," tweeted the journalist Ricardo Arrúa.

The rancour against her was evident on Argentinian Twitter feeds. "How beautiful, Margaret Thatcher died," said Santi Cuestas, a young football fan of Argentina's Boca team. The well-known Argentinian cinema critic Eduardo Antin was dismissive: "Nothing like Twitter to stay informed of news that doesn't interest us."

"Argentina's dictators drooled over her," wrote the columnist Alberto Amato in the mass daily Clarín, recalling how Argentina's generals applauded when Thatcher reacted coolly to the death of the IRA member Bobby Sands during a hunger strike at Maze prison in 1981, when she said: "He chose to take his own life; it was a choice that his organisation did not allow to many of its victims." Thatcher's statement was praised by Argentina's military dictatorship, which at that time was involved in a murderous campaign to eliminate leftwing activists. But a year later, at the receiving end of Thatcher's steely determination, "Thatcher's ferocity was condemned by those who had before applauded it," Amato wrote.

Another Argentinian expressed gratitude for Thatcher's victory over the generals in the 1982 war, a humiliating defeat that forced them to abandon power a year later. "Thankyou Maggie Thatcher, for catalyzing the return of democracy in Argentina," wrote Andres Wolberg-Stok, who covered the war for the Buenos Aires Herald as a young reporter 31 years ago, on his Facebook account.